Answer:
6 ± i and 6 ± i
Step-by-step explanation:
Let x be the first number.
Let y be the second number.
x + y = 12
x × y = 37
Solve for x in the first equation.
x = 12 - y
Put x as 12-y in the second equation and solve for y.
(12- y)y = 37
12y - y² = 37
- y² + 12y - 37 = 0
y = 6 ± i
Put y as 6 ± i in the first equation and solve for x.
x + 6 ± i = 12
x = 12 - 6 ± i
x = 6 ± i
Answer:

Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
In this problem line AB and line BC are perpendicular
so

step 1
Find the slope AB
we have
A(p,4), B(6,1)
The formula to calculate the slope between two points is equal to

substitute the values


step 2
Find the slope BC
we have
B(6,1), and C(9,q)
The formula to calculate the slope between two points is equal to

substitute the values


step 3
Find the equation that relates p and q
we know that

we have


substitute



Answer:
x > − 6
Step-by-step explanation:
Yes, the volume it is 8³ = 512
The volume it is 420
512 >>> 420
The side the cube is ³√420 = 7.48 in
8 >> 7.44
Answer:
129.996 cubic feet
Step-by-step explanation:
Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

First, we have to find the radius, which is:
D = 2r
So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.

Now, we solve. Exponents are first...
3.14(9)(4.6)
Now multiply left to right.
28.26(4.6)
129.996 cubic feet
Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!